292 Mr. William Sutherland on the 



18. An Attempt to Determine the Velocity of Light through 

 the substance of the water-molecule. — In spite of the excep- 

 tions, the relation demonstrated in Table XXXIX. is suffi- 

 ciently striking. To explain it, let us replace q by its value 

 (N — 1)U ; then, in interpreting the expression u — (N — 1)U 

 as occurring in our expression for the conductivity of a solu- 

 tion, there are two methods of procedure : first, we can assume 

 that u — U, the free or unoccupied part of the domain, is the 

 most likely to occur, in which case N= 2 ; second, that u — cJJ 

 occurs in the expression for conductivity, and that c happens 

 to have the same value as N — 1, on which supposition it would 

 be desirable to determine N. At present I know of only one 

 way of attempting to find N or v/Y, the ratio of the velocity 

 of light through free aether to its velocity through the matter 

 of an atom, namely by means of Fizeau's experiment, repeated 

 by Michel son and Morley, on the fraction of its motion com- 

 municated by flowing water to light passing through it. 

 Exactly in the manner of my paper (Phil. Mag. Feb. 1889, 

 p. 148) we can estimate the effect of the motion of matter on 

 the light passing through it. Let s be the distance travelled 

 by light in water flowing through the aether at rest with 

 a velocity 8 in the same direction as the light, v' 1 the mean 

 velocity of light through the flowing water, v' the mean 

 velocity through still water, v its velocity through free aether, 

 Y through a molecule of water, I the mean distance through 

 a molecule, and a its mean sectional area ; then the total loss 

 of time experienced by a wave of unit area of front or a tube 

 of parallel rays, or, briefly, a ray of unit section in passing 

 through the matter-strewn path s instead of a clear path in free 

 aether, will be equal to its loss in a molecule multiplied by the 

 number of molecules passed through in the path. This 

 number, when the matter is at rest, is proportional to s, to a, 

 and to p/M, or it varies as sap/M. ; but when the matter is in 

 motion it is reduced in the ratio 1 — 8/v": 1. The loss of time 

 in each molecule is found thus : l/Y is the time taken to pass 

 through a molecule, and in this time the molecule moves 

 a distance 18/Y and the unit wave-front moves a distance 

 1(1 + S/Y) , which in free aether would take a time 1(1 + S/Y)/v ; 

 so that the loss of time in a molecule is l/Y — l(l + 8/Y)/v. 

 Hence, the total loss of time in the path s may be written 



1+* 



ksalp / 1 T VW 8\ 



m \y ~r~)\ l ~w)' 



But the loss of time is also s/v"— s/v ; equating the two ex- 



